Problem: Add $10_7 + 163_7.$ Express your answer in base 7.
Explanation: We can line up the numbers and add just as we do in base 10.  For example, in the second column we get $1+6=7$, which we carry just as in base 10 by placing the digit 0 in the sum and carrying 1 to the next column. We get $$
\begin{array}{c@{}c@{}c@{}c}
& & 1 & 0_7 \\
+ & 1 & 6 & 3_7 \\
\cline{2-4}
& 2 & 0 & 3_7, \\
\end{array}$$so the sum is $\boxed{203_7}$